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Exercise 39 - Chapter 3

Consider the free categories \( C = [ \cdot \rightarrow \cdot ] \) and \( D =[ \cdot \rightrightarrows \cdot ] \) . Give two functors \( F, G : \mathcal{C} \rightarrow \mathcal{D} \) that act the same on objects but differently on morphisms.

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  • 1.

    Both \(F: C \to D\) and \(G: C \to D\) can map the left point to the left point, and the right point to the right point. But they can differ by having \(F\) map the one morphism in \(C\) to the top morphism in \(D\) and having \(G\) map the one morphism in \(C\) to the bottom morphism in \(D\).

    Comment Source:Both \\(F: C \to D\\) and \\(G: C \to D\\) can map the left point to the left point, and the right point to the right point. But they can differ by having \\(F\\) map the one morphism in \\(C\\) to the top morphism in \\(D\\) and having \\(G\\) map the one morphism in \\(C\\) to the bottom morphism in \\(D\\).
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